6 research outputs found
Disjoint Total Dominating Sets in Near-Triangulations
We show that every simple planar near-triangulation with minimum degree at
least three contains two disjoint total dominating sets. The class includes all
simple planar triangulations other than the triangle. This affirms a conjecture
of Goddard and Henning [Thoroughly dispersed colorings, J. Graph Theory, 88
(2018) 174-191]